x | y |
---|---|
2 | 10 |
4 | 8 |
10 | 3 |
15 | 1.5 |
Could you model this data with a direct variation?
No; the ratio of corresponding x- and y-values are not constant.
A plot of the points suggests that an inverse relationship is possible. Test to see whether the products of x and y are constant.
Since the products are not constant, the relationship is not an inverse variation.
Is the relationship between the variables a direct variation, an inverse variation, or neither? Write function models for the direct and inverse variations.
Direct and Inverse Variation
x | y |
---|---|
0.2 | 8 |
0.5 | 20 |
1.0 | 40 |
1.5 | 60 |
x | y |
---|---|
0.2 | 40 |
0.5 | 16 |
1.0 | 8.0 |
2.0 | 4.0 |
x | y |
---|---|
0.5 | 40 |
1.2 | 12 |
2 | 10 |
2.5 | 6 |
Suppose x and y vary inversely, and x = 4 when y = 12.
What function models the inverse variation?
The function is
What does the graph of this function look like?
Make a table of values. Sketch a graph.
Is it reasonable to connect the points of this function with a smooth curve?
Yes,
x | y |
---|---|
3 | 16 |
4 | 12 |
6 | 8 |
8 | 6 |
12 | 4 |
16 | 3 |
What is y when x = 10?